Support of canonical space-time measure for Brakke flows is parabolic (k+2)-rectifiable, implying unique tangent flows and density agreement a.e., with equivalence of standard and space-time-Grassmann convergence.
Equality of the usual definitions of Brakke flow
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abstract
In 1978 Brakke introduced the mean curvature flow in the setting of geometric measure theory. There exist multiple variants of the original definition. Here we prove that most of them are indeed equal. One central point is to correct the proof of Brakke's \S 3.5, where he develops an estimate for the evolution of the measure of time-dependent test functions.
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math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Parabolic rectifiability of the Brakke flow
Support of canonical space-time measure for Brakke flows is parabolic (k+2)-rectifiable, implying unique tangent flows and density agreement a.e., with equivalence of standard and space-time-Grassmann convergence.